When for example in a numerical cell an invalid value is entered eg: "6666666666666666666666666666666666", and enter is pressed, the exception is shown (value 6666666666666666666666666666666666 not valid for field x) correctly, but when pressing enter on the exception, it becomes to show until you press escape twice.

With the mouse there are also problems, in the same case of an invalid value in a cell, after entering the value (without pressing enter), if we try to move the focus to another cell, the corresponding exception is raised, but the focus of the invalid cell is lost and passes the focus to the cell indicated by the mouse, leaving the cell that caused the exception, out of focus.

The behavior in all cases should be that if a cell is not valid you should never lose focus, in other words if you try to move the focus (by any means) of an invalid cell you should go back to that cell's editor, to allow to correct the error or cancel the changes with Esc.
Puede observar este comportamiento en su demo: \Steema Software\Steema TeeGrid for VCL & FMX Registered version-1.05\demos\FireMonkey\Database\DataSet\TeeGrid_FMX_DataSet_Demo.dpr

You can see in this demo: \ Steema TeeGrid for VCL & FMX Registered version-1.05 \ demos \ FireMonkey \ Cell Editors \ TeeGrid_FMX_Cell_Editors.dproj, that the behavior is more similar to the correct, I imagine it will be because data is not a descendant of TDataSet.

PD:
I remind you that this behavior has only been tested in FMX.Win32.Seattle